Multiplying by 2-Digit Numbers

Multiply the ones (3 x 6 = 18). Write
8 in the ones' place and carry the 1 forward to the tens'

5 8 6
x 2 3

18

Multiply the tens and add what was carried forward
(3 x 8 = 24 + 1 = 25). Write 5 in the tens' place and carry the
2 forward to the hundreds'

5 8 6
x 2 3

2518

Multiply the hundreds and add what was carried forward
(3 x 5 = 15 + 2 = 17). Write 7 in the tens' place and the
1 forward in the thousands'

5 8 6
x 2 3

1
72518

Add a zero* and multiply the ones (2 x 6 = 12).
Write 2 in the tens' place and carry the 1 forward to the hundreds'

5 8 6
x 2 3

1
7251812 0

Multiply the tens and add what was carried forward
(2 x 8 = 16 + 1 =17). Write 7 in the hundreds' place and carry
the 1 forward to the thousands'

5 8 6
x 2 3

1
725181712 0

Multiply the hundreds' and add what was carried
forward (2 x 5 = 10 + 1 =11). Write 1 in the thousands place and
1 in the ten thousands'

5 8 6
x 2 3

1
725181 11712 0

Add the two products to get the answer.

5 8 6 x 2 3

1
725181 11712 0

1 3 4 7 8

586 x 23 = 13478

* We really wanted to multiply by 20,
not 2. Adding a zero and multiplying by 2 is the same as multiplying
by 20.

Common error when multiplying

When using the method above to multiply numbers with two or more digits, it is important that students understand where and why they must add zeros. The example below shows a fairly common error that students who do not fully understand the process can make.

As with most calculations, estimating to check whether the calculated answer is reasonable is a good way to catch errors like the made above.

Worksheets

Try the worksheets below for more practice with multiplying by 2-digit
numbers.